Related papers: Complexity, Statistical Risk, and Metric Entropy o…
Estimation of a regression function from independent and identically distributed data is considered. The $L_2$ error with integration with respect to the distribution of the predictor variable is used as the error criterion. The rate of…
Thevon Neumann entropy, named after John von Neumann, is an extension of the classical concept of entropy to the field of quantum mechanics. From a numerical perspective, von Neumann entropy can be computed simply by computing all…
This paper studies generalization error bounds for Transformer models. Based on the offset Rademacher complexity, we derive sharper generalization bounds for different Transformer architectures, including single-layer single-head,…
The paper presents a generalization bound for quantum neural networks based on a dynamical Lie algebra. Using covering numbers derived from a dynamical Lie algebra, the Rademacher complexity is derived to calculate the generalization bound.…
In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that…
We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number…
ReLU neural-networks have been in the focus of many recent theoretical works, trying to explain their empirical success. Nonetheless, there is still a gap between current theoretical results and empirical observations, even in the case of…
We consider the optimization problem associated with fitting two-layers ReLU networks with respect to the squared loss, where labels are generated by a target network. We leverage the rich symmetry structure to analytically characterize the…
Recent years have witnessed a resurgence in using ReLU neural networks (NNs) to represent model predictive control (MPC) policies. However, determining the required network complexity to ensure closed-loop performance remains a fundamental…
We study deep ReLU feed forward neural networks (NN) and their injectivity abilities. The main focus is on \emph{precisely} determining the so-called injectivity capacity. For any given hidden layers architecture, it is defined as the…
"Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This dramatic success of deep learning in the last few years has been hinged on an enormous…
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…
We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating…
Statistical learning theory provides bounds on the necessary number of training samples needed to reach a prescribed accuracy in a learning problem formulated over a given target class. This accuracy is typically measured in terms of a…
Neural networks with REctified Linear Unit (ReLU) activation functions (a.k.a. ReLU networks) have achieved great empirical success in various domains. Nonetheless, existing results for learning ReLU networks either pose assumptions on the…
This work introduces the first toolkit around path-norms that fully encompasses general DAG ReLU networks with biases, skip connections and any operation based on the extraction of order statistics: max pooling, GroupSort etc. This toolkit…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut…
While previous optimization results have suggested that deep neural networks tend to favour low-rank weight matrices, the implications of this inductive bias on generalization bounds remain underexplored. In this paper, we apply Maurer's…
We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $\mathbb{R}^d$ with respect to the square loss. Our main result is an efficient algorithm for this learning task…